Basic Calculations Review - University of North Carolina ...

Basic Calculations Review

I.

Okay. It has been a long time since we have had to even THINK about Roman numerals vs.

Arabic numerals, right? So just to refresh, a Roman numeral looks like this "XVI" but an

Arabic numeral looks like this "16." In pharmacology, the apothecary system requires that

we understand the use of both Roman and Arabic numerals. Just to refresh your memory,

here are the commonly used Roman numerals:

I = 1 V = 5 X = 10

L = 50 C = 100 D = 500

M = 1000

Here is an entire Roman Numeral table:

1 I 2 II 3 III 4 IV 5 V 6 VI 7 VII 8 VIII 9 IX 10 X 11 XI 12 XII 13 XIII

Roman Numeral Table

14 XIV

27 XXVII

150 CL

15 XV

28 XXVIII

200 CC

16 XVI

29 XXIX

300 CCC

17 XVII

30 XXX

400 CD

18 XVIII

31 XXXI

500 D

19 XIX

40 XL

600 DC

20 XX

50 L

700 DCC

21 XXI

60 LX

800 DCCC

22 XXII

70 LXX

900 CM

23 XXIII

80 LXXX

1000 M

24 XXIV

90 XC

1600 MDC

25 XXV

100 C

1700 MDCC

26 XXVI

101 CI

1900 MCM

Let's review some Roman numeral rules:

FIRST: You cannot repeat a Roman numeral over three times. In otherwords, if you want to write the Arabic number "30" as a Roman numeral, you can do it like this: XXX. But if you want to write the Arabic number "40" as a Roman numeral, XXXX would be incorrect. Instead, you would document XL. Why? Well, when you place a smaller Roman numeral in front of a larger Roman numeral, this indicates subtraction. So in our "XL" example, X=10 and L=50. So really, I am saying 50-10 = 40. You do a few:

1. IV = _____________ 2. IX = _____________ 3. CD = _____________

SECOND: If smaller numerals follow larger ones, then you add. The same no repeating more than three in a row still applies. So if I want to express the number "11", I write XI. For "12" I document XII. For "15" I write XV and so on. You try a few:

1. Express 16 as a Roman numeral: _____________ 2. Express 25 as a Roman numeral: _____________ 3. Express 31 as a Roman numeral: _____________

THIRD: There are a few oddities with Roman numerals but the one most typically seen in pharmacology is the use of ? which is expressed as ss often with a line over the top.

FOURTH: In pharmacology/dosage calculations, you would rarely need to use an of the higher Roman numerals.

Here is an example of what an order might look like using Roman numerals:

Give Seconal sodium gr iss p.o. stat

II. Now, on to reducing fractions. On your mathematics pretest, the primary issue was one of not knowing how to reduce fractions, it was in following directions. The directions indicated that you were to reduce the fractions to their lowest terms. Many of you stopped before you got to the final answer. For example, 24/30. Many of you gave an answer of 12/15 which is not the lowest terms. Instead, the correct answer was 3/5. This was an issue throughout the test. BE CAREFUL. Not following directions, to the letter, can not only result in test failure but more importantly, patient death.

Let's practice some fraction reduction. Your directions are to reduce the following

fractions to the lowest terms:

1. 4/22

__________________

2. 24/40

__________________

3. 207/90 __________________

4. 20/24

__________________

5. 88/18

__________________

III. Onward and upward! Let's talk about adding and subtracting fractions. Remember. While you will have use of a calculator, it is a basic functions calculator which will not have the nice a/b fraction key. You have to know how to do this the old fashioned way. That goes for a lot of the problems. Don't become over confident because you have a calculator in hand because it will be useless if you do not know mathematics basics or how to correctly set up the problem.

I am sure that we all have our own way of adding and subtracting fractions but let me show you the easy way. Besides...why work harder when you can work SMARTER!

Let's say you have this problem:

2/5 + 1/9 = ? Well, you know we have to find a common denominator and all that time consuming stuff, right? Nope. All you have to do is multiply each side by the denominator of the other. Like this:

2x9 +1x5 5x9 9x5

You get 18/45 + 5/45 = 23/45! No more searching for that least common denominator!

Let's do another one:

44 + 1 10 9

44 x 9 1 x 10 10 x 9 + 9 x 10

You get 396/90 + 10/90 = 406/90 which is an improper fraction, right? So we have to reduce it to 4 and 46/90 or 4 23/45. See how easy that is! And it works for subtraction as well. Let's look:

11 - 6 The goal is to make the denominators the same using the same technique above: 8 5

11 x 5 - 6 x 8 8 x5 5x8

You get 55/40 ? 48/40 = 7/40 VIOLA!

IV. Now--multiplying and dividing fractions is a bit trickier. To multiply a fraction, we just multiply straight across, right? So:

3 x 10 Well, I can just multiply across and get 30/44 and then reduce. Or.... 4 11

I could make my numbers a little smaller and easier to work with by reducing first: (5)

3 x 10 = 15/22 4 11 (2)

Next, dividing fractions. When you divide fractions, you have to do what I call "the flip." For example, let's say you are asked to complete the following:

1/4 ? 1/5 = ?

You actually have to rewrite or "flip" the second fraction (now it is called the reciprocal). The problem then becomes a multiplication problem and looks like this:

1/4 x 5/1 = 5/4 or 1 1/4

Let's do another one:

1/6 ? 1/8 = ?

1/6 x 8/1 = 8/6 or 1 2/6 then 1 1/3 reduced to its lowest term. Right?

You practice a few:

1. 1/200 ? 1/300 = ____________________ 2. 2/3 ? 5/7 = ____________________ 3. 1 5/8 ? 9/27 = ____________________ 4. 2/9 ? 3/12 = ____________________

V. The next section on the math pretest also caused an issue due to not following directions. You were asked to "Change the following fractions to decimals; express your answer to the nearest tenth." Before I go on, let's review decimal places:

millions

9,000,000.0

hundred thousands 900,000.0

ten thousands

90,000.0

thousands

9,000.0

hundreds

900.0

tens

90.0

ones

9.0

tenths

0.9

hundredths

0.09

thousandths

0.009

ten thousandths

0.0009

hundred thousandths

0.00009

millionths

0.000009

So, when you were asked to change 6/7 to a decimal and express your answer to the nearest tenth, many of you provided .85 as the answer. Actually, it is 0.85 rounded to the nearest tenth as 0.9. Remember I told you that in our program, we put the zero in front of the decimal do avoid confusion. Do not forget to

put it there because your answer will be marked incorrect! The 0.85 would be correct if you were asked to round to the nearest hundredths.

VI. Next we need to look at identifying which fraction has the largest value. Actually, there are two ways to do this. One is to simply change the fraction to a decimal. Let's look at the following:

3 or 4 4 5

0.75 0.80 The 8 is bigger than the 7 so 4/5 is the larger of the two fractions.

The other way to do this is to multiply the denominator of the first fraction by the numerator of the second fraction and repeat with the second fraction. Like this:

(15) (16)

3

4

4

5

So again, 16 is bigger than 15 so 4/5 is correct! Don't you wish they would have made it this easy is school! Let's practice a few. Use either method you would like. Which has the greatest value:

1. 1/100 or 1/150: ___________________ 2. 3/7 or 1/2 : ___________________ 3. 13/20 or 3/5: ___________________ 4. 1/4 or 1/10: ___________________

VII. Okay. Adding, subtracting and multiplying decimals. Easy stuff!

Adding 1.452 + 1.3

Line the decimals up: 1.452 + 1.3

"Pad" with zeros:

1.452 + 1.300

Add:

1.452 + 1.300

2.752

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download